1.118
m/s
2.2361
m^3/s
0.01782
1.118
m/s
1.118
m/s
2.2361
m^3/s
0.01782
1.118
m/s
The Chezy Formula Calculator computes the mean flow velocity and discharge in an open channel using the Chezy equation, one of the earliest rational formulas in hydraulic engineering. Proposed by Antoine de Chezy in 1769 for the design of the Paris water supply canal, it remains a foundational equation in fluid mechanics: $$v = C\sqrt{R_h S}$$ where C is the Chezy coefficient, R_h is the hydraulic radius, and S is the channel slope.
While Manning's equation has largely superseded Chezy's in everyday practice, the Chezy formula holds historical and theoretical significance. It follows directly from dimensional analysis and the balance of gravitational and frictional forces. The Chezy coefficient C is related to Manning's n by: $$C = \frac{R_h^{1/6}}{n}$$
This calculator also reports the equivalent Manning's n for cross-reference. The Chezy formula is used in river hydraulics, sediment transport modeling, and computational fluid dynamics codes that parameterize bottom friction with a Chezy-type law.
The Chezy formula is derived from balancing the gravitational component driving flow down a slope against the bed shear stress retarding it:
$$\tau_0 = \rho g R_h S$$ Setting this equal to the shear stress expressed as $$\tau_0 = \frac{\rho g}{C^2} v^2$$ and solving for velocity: $$v = C\sqrt{R_h S}$$
Discharge: $$Q = A \cdot v = A \cdot C\sqrt{R_h S}$$
Relation to Manning's n: $$C = \frac{R_h^{1/6}}{n}$$ This means the Chezy coefficient depends on both roughness and depth, while Manning's n depends primarily on roughness alone — one reason Manning's formula became more popular.
Typical C values: Smooth concrete: 70–80 | Earth channel: 40–50 | Natural river: 30–40 | Rough mountain stream: 15–25
A higher Chezy coefficient indicates a smoother, more hydraulically efficient channel. Velocity increases with both the hydraulic radius (deeper flow in efficient cross-sections) and the slope. Unlike Manning's n, where a smaller value means smoother flow, the Chezy C works in the same direction as velocity — larger C gives faster flow. The equivalent Manning's n output helps you cross-reference with the more commonly used Manning framework.
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A concrete canal (C = 70) with Rh = 0.6 m and 0.1% slope yields v ≈ 1.71 m/s. The equivalent Manning's n ≈ 0.013 confirms a smooth channel.
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A natural channel (C = 40) with Rh = 0.8 m and gentle slope flows at 0.80 m/s. Manning's n ≈ 0.024 indicates clean earth.
The Chezy coefficient C (units: m^½/s) is a resistance parameter in the Chezy formula v = C√(Rh·S). It encapsulates the roughness of the channel boundary. Higher C means less resistance (smoother channel). Unlike Manning's n, C also varies with depth through its dependence on Rh.
They are mathematically equivalent. Manning's equation v = (1/n)Rh^(2/3)S^(1/2) can be rewritten as v = C√(Rh·S) where C = Rh^(1/6)/n. The key difference is that Manning's n is nearly constant for a given channel, while C varies with depth.
Antoine de Chezy (1718–1798) was a French hydraulic engineer who developed his formula around 1769 while designing a canal to supply water to Paris. His work was among the first to apply rational analysis to open-channel flow, predating Manning by over a century.
Manning's roughness coefficient n depends primarily on the channel surface and is nearly constant regardless of flow depth. The Chezy C varies with depth (through Rh^(1/6)), making it less convenient for design. Manning's equation also has more extensive published tables of n values.
Yes, the Chezy formula applies to any uniform flow situation, including partially filled pipes with a free surface. For full pressurized pipes, it is equivalent to the Darcy-Weisbach equation with an appropriate conversion between C and the friction factor f.
You can convert from Manning's n using C = Rh^(1/6)/n. Alternatively, empirical formulas exist: Bazin's formula C = 87/(1 + γ/√Rh) and Kutter's formula are commonly used. The simplest approach is to look up n from published tables and convert.
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